CASE STUDY Vehicle Cash-Back Incentives facturers are offering special deals to sell off the current year's vehicles beemanu. models arrive. Karim's local Ford dealership is advertising 3.9% financ months (i.e., 3.9% compounded monthly) or up to $4000 cash back on sel Karim Soltan is shopping for a new vehicle, and has noticed that many vehi. efore the ing fora ene selected vehi for a full 48 FVg The vehicle that Karim wants to purchase costs $24 600 includin licence, and dealer preparation. This vehicle qualifies for $1800 cash back if cash for the vehicle. Karim has a good credit rating and knows that he cou vehicle loan at his bank for the full price of any vehicle he chooses. His to take the dealer financing offered at 3.990 for 48 months wh pays ld a rran r option is PA Karim wants to know which option requires the lower monthly payment. Heknom he can use annuity formulas to calculate the monthly payments Ows For QUESTIONS 1. Suppose Karim buys the vehicle on July 1. What monthly payment must Karim make if he chooses the dealers 3.9% financing option and pays off the loan over 48 months? (Assume he makes each monthly payment at the end of the month and his first payment is due on July 31.) 2. Suppose the bank offers Karim a 48-month loan with the interest compounded monthly and the payments due at the end of each month. If Karim accepts the bank loan, he can get $1800 cash back on this vehicle. Karim works out a method to calculate the bank rate of interest required to make bank financing the same cost as dealer financing. First, calculate the monthly rate of interest that would make the monthly bank payments equal to th monthly dealer payments. Then calculate the effective rate of interest represented by the monthly compounded rate. If the financing from the bank is at a lower rate of interest compounded monthly, choose the bank financing. The reason is that the monthly payments for the bank's financing would be lower than the monthl payments for the dealer's 3.9% financing (a) How much money would Karim have to borrow from the bank to pay cast for this vehicle? (b) Using the method above, calculate the effective annual rate of inte rest a nominal annual rate of interest required to m bank financing exactly the same as for dealer financing ake the monthly payment SUMMARY OF FORMULAS 461 3. Suppose Karim d ecides to explore the costs of financing a more expensive vehicle. .9% dealer The more expensive vehicle costs $34 900 in total and qualifies for the financing for 48 months or $2500 cash back. What is the highest effective annual rate of interest at which Karim should borrow from the bank instead dealer's 3.9% financing? 3